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A309150 Number of solutions of the Diophantine equation 1/n + 1/x = 1/y + 1/z, where n >= 1, x > n, y > n and z > y. 1

%I

%S 0,2,7,12,20,29,27,41,52,60,48,101,51,96,134,93,62,142,71,209,176,114,

%T 79,264,134,136,176,256,99,363,88,217,262,178,368,406,100,180,311,469,

%U 119,471,113,386,508,182,116,552,223,353

%N Number of solutions of the Diophantine equation 1/n + 1/x = 1/y + 1/z, where n >= 1, x > n, y > n and z > y.

%e n=2: 1/2 + 1/12 = 1/3 + 1/4, 1/2 + 1/30 = 1/3 + 1/5.

%t a[n_]:=Length@Solve[1/(n)+1/(x)==1/y+1/z&&x>n&&z>y&&y>n,{x,y,z},Integers];

%t Array[a,50]

%Y Cf. A309149, A063647, A018892.

%K nonn

%O 1,2

%A _S. Nazardonyavi_, Jul 14 2019

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Last modified June 25 01:53 EDT 2021. Contains 345445 sequences. (Running on oeis4.)